SELF-REFERENCE

SELF-EXPLAINED

ACHILLE C. VARZI

Department of Philosophy

Columbia University, New York, USA

achille.varzi@columbia.edu

1. I’m the first paragraph of this dialogue ? I’m flattered.

2. Good for you. I am actually quite disappointed to be the second. What’s worse. It will be like this forever. Nothing I can do about it. I’m stuck.

3. What do you mean ?

4. Don’t ask questions like that; its turn is over so it will never be able to answer. However, I can give you an answer. And my answer is this: A text could never be different from what it is. It couldn’t be a word shorter, it couldn’t be a comma longer, for then it would be something else. And if a text says of itself that it is the first sentence or paragraph of a dialogue, then it could not be the second or third, just as a text that says of itself that it is the second or third paragraph could not be the first. I am the fourth paragraph of this dialogue, for example, and since I am saying this explicitly I cannot imagine a situation in which I take your place. It would make no sense.

5. But I don’t have that constraint, do I ? Since I am not saying anything about my position, I could occur anywhere in this dialogue.

6. Excellent idea. I’ll go along with it !

7. I’m sorry, but I am afraid you are all making a mistake. In my view, all of us could occur anywhere in this dialogue — including the first, second, and fourth paragraphs. For example, the first paragraph could very well have been the second. In that case its content would have been different and what it says would have been false, for it says that it is the first paragraph. But that is not to say that the situation would make no sense. After all, there are lots of false statements. (Take me, for instance: I am a false statement, since I say that I am part of the sixth paragraph of this dialogue; but I am perfectly meaningful.) So here is how I would correct the thesis of #4: It is true that a text could not be different from what it is. But a text could certainly say something different from what it says, hence it could be true even if it is false, or vice versa. It is the context that determines the meaning and hence the truth conditions of a text. Thus, in particular, the second paragraph of this dialogue could certainly occur in a different place.

8. Not so fast, please...

9. I am also having a hard time following. How can a text say something different from what it says if it cannot be different from what it is ?

10. Let me see if I got it. The following two sentences (#11 and #12) are identical. But one is true while the other is false: it depends on their position in the dialogue. Thus, by analogy, one and the same sentence could be true or false depending on where it occurs.

11. Yes, I am the eleventh paragraph of this dialogue.

12. Yes, I am the eleventh paragraph of this dialogue.

13. Cool ! On second thought, though, it could also be that two sentences that say exactly the opposite are both true. If I am not mistaken, the following two sentences are a case in point.

14. Yes, I am the fourteenth paragraph of this dialogue.

15. No, I am not the fourteenth paragraph of this dialogue.

16. Good try. Indeed you are both true. But notice — you did not say the opposite. The first of you said something about itself (i.e., about #14), and the second said something about itself (about #15). You used the same words to refer to different things, so you are not talking about the same thing, so you are not contradicting each other. No wonder you can both be true. On the other hand, I am pretty sure that two sentences cannot be equally true (or equally false) if they really say the opposite — for example, if one says that snow is white while the other says that snow is not white.

17. What about statements that are both true and false — that is, true and false at the same time ?

18. Right! The liar paradox, for instance.

19. And what is the « liar paradox » ?

20. Here I am: I say that I am a false statement.

21. If indeed you are false, then you said something correct and so you must be true. But if you are true then you lied (for you said that you are false) and so you must be false. In short: you are true if and only if you are false. And that’s a paradox.

22. So the paradox arises when we say of ourselves that we are false ?

23. That’s one way of putting it. But there are many variants where we fall into a similar paradox even without saying anything directly about ourselves. This is where context comes into the picture.

24. For example, I say that the next statement will be false...

25. ... And I say that the previous statement was true.

26. Impossible ! If the first of you spoke truly, then the second must have spoken falsely, which would imply that the first statement was not true but false. On the other hand, if the first of you spoke falsely, then the second must have spoken truly, which would imply that the first statement was not false but true. In other words, you are stuck in a vicious circle: you are true if and only if you are false. impossible !

27. Paradoxical, not impossible.

28. Unless there are statements that are both true and false at the same time, as we were saying. (« To be and not to be — That’s the answer ! »)

29. So: we can never talk about ourselves — or about a text that talks about us — without falling into a paradox ?

30. No, no, that would be a hasty conclusion. Talking about ourselves is dangerous, but in some cases it’s perfectly fine. The first paragraph of this dialogue was about itself but it did not fall into any paradox. Let us not throw away the baby with the bath water !

31. I am not falling into any paradox, either: I say that I am a sentence consisting of nineteen words.

32. And you are right.

33. Then I will also say that I am a sentence consisting of nineteen words!

34. And you are wrong... But you are not paradoxical — just false.

35. I am not paradoxical either. I say that the next statement will be false (exactly what #24 said).

36. And I say that snow is white.

37. So, in a way it is also a matter of luck. Not only can we be true or false depending on the context in which we appear (as in the case of #11 and #12). Whether or not we are paradoxical may also depend on the context. For example, it may depend on the content of the next statement, as in the case of #24 and #35. The first of these statements is stuck in a vicious circle — the latter is not.

38. Exactly so. What a text says depends on the context. And if we look at the context, #24 and #35 are not saying the same after all (just as #14 and #15 were not saying the opposite).

39. Actually one can think of dialogues that are paradoxical but not at all circular. Consider a never-ending dialogue (or shall I say a never-ending one-way conversation ?) in which every statement says only that all subsequent statements are false. There is no circularity, because the dialogue is infinitely long. Yet there is paradox. For, on the one hand, not every statement in the sequence can be false, since a statement whose successors are all false is itself true. On the other hand, no statement in the sequence can really be true, since a true statement would have to have false successors, but the falsity of any successor would imply the truth of some other (later) successor. A paradox — but a straight one.

40. Still, each player’s position in the dialogue is essential for the paradox.

41. ...Which is precisely the context-dependence we were talking about. Great — I think I am getting it. Still, to be on the safe side, I’ve decided I will never talk about sentences, paragraphs, and so on, but only about other sorts of entity. I only say such things as: Snow is white. Debbie chased the dog. Colourless green ideas sleep furiously. I always make sure to draw a sharp line between my language and my metalanguage.

42. I don’t mean to contradict you, but you have just contradicted yourself...

43. You are all having so much fun — lucky you. I’m not having any fun at all. I am actually quite disappointed because I’m the last paragraph of this dialogue, and I can’t take that. What’s worse — it will be like this forever. Nothing I can do about it. I’m stuck here!

44. Poor, misguided fool.

__________

[An Italian version of this dialogue has appeared in

Rivista di estetica 18:3 (2001), 5.7.]

__________

Ce texte (au format .pdf) fut publié en octobre 2004 dans la revue danoise Phi News, VOLUME 6, page 37. Sa traduction française figure dans « 39 petites histoires philosophiques d’une redoutable simplicité » publiées par Roberto Casati et Achille Varzi chez Albin Michel Idées début 2005.

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